The title said it, what is:
$$
\lim_{x\to 0} \frac{e^{2x}-x^2+x}{\cos(x)-1} = ~?
$$
If I evaluate the term I get $1/0$, by looking at a graph I see that it goes to $-\infty$, but I don't now how evaluate the limit?

what you mean by limit is $0^{-}$? i think the limit is just $0$ in the usual definition of limit...
–
StefanFeb 1 '13 at 19:58

I mean the limit is $0$, with negative values close to $0$ (and for all $x\neq 0$ actually here). It approaches $0$ from the left, if you prefer. Like when you distinguish the left limit and the right limit at some point.
–
1015Feb 1 '13 at 20:03